Function Repository Resource:

# ReuleauxPolygon

Represent a Reuleaux polygon

Contributed by: Jan Mangaldan
 ResourceFunction["ReuleauxPolygon"][n] gives the Reuleaux polygon constructed from n vertices equally spaced around the unit circle. ResourceFunction["ReuleauxPolygon"][r,n] gives the Reuleaux polygon based on a regular polygon of radius r. ResourceFunction["ReuleauxPolygon"][{r,θ},n] starts at angle θ with respect to the x axis. ResourceFunction["ReuleauxPolygon"][{x,y},rspec,n] centers the Reuleaux polygon at {x,y}.

## Details

A Reuleaux polygon is a polygon of constant width made up of circular arcs of constant radius.
n must be a positive odd integer.
The angle θ is measured in radians counterclockwise from the positive x-direction.
ResourceFunction["ReuleauxPolygon"] returns a FilledCurve object and can be used as a graphics primitive.

## Examples

### Basic Examples (2)

A Reuleaux triangle:

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Different styles applied to ReuleauxPolygon:

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### Scope (4)

Generate a Reuleaux triangle, pentagon, heptagon, etc.:

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Generate Reuleaux pentagons of varying radii:

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Generate Reuleaux triangles of varying starting angles:

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FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:

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### Properties and Relations (1)

ReuleauxPolygon uses the same vertices as RegularPolygon:

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### Neat Examples (1)

A collection of random Reuleaux polygons:

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## Version History

• 1.0.0 – 06 December 2021